Generalised Jantzen filtration of Lie superalgebras I

@article{Su2010GeneralisedJF,
  title={Generalised Jantzen filtration of Lie superalgebras I},
  author={Yucai Su and R. B. Zhang},
  journal={arXiv: Representation Theory},
  year={2010}
}
A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan-Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of… 
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15 Citations
Highly Influential Citations
2
Background Citations
5
Methods Citations
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15 Citations

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References

SHOWING 1-10 OF 51 REFERENCES
Generalised Verma modules for the orthosymplectic Lie superalgebra osp(k|2)
Super duality and Kazhdan-Lusztig polynomials
We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a…
Composition factors of Kac modules for the general linear Lie superalgebras
The composition factors of Kac modules for the general linear Lie superalgebras are explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys. 33 (1992),…
Highest weight categories arising from Khovanov's diagram algebra III: category O
We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although…
Filtrations on generalized Verma modules for Hermitian symmetric pairs.
The purpose of this paper is to analyze filtrations on generalized Verma modules for Hermitian Symmetrie pairs. We prove that the socle and radical series for these modules coincide and explicitly…
Cohomology of Lie superalgebras 𝔰𝔩m|n and 𝔬𝔰𝔭2|2n
We explicitly compute the first and second cohomology groups of the classical Lie superalgebras 𝔰𝔩m|n and 𝔬𝔰𝔬 2|2n with coefficients in the finite‐dimensional irreducible modules and the Kac…
Character and dimension formulae for general linear superalgebra
On the composition factors of Kac modules for the Lie superalgebras sl(m/n)
In the classification of finite‐dimensional modules of Lie superalgebras, Kac distinguished between typical and atypical modules. Kac introduced an induced module, the so‐called Kac module V(Λ) with…
Highest Weight Categories Arising from Khovanov's Diagram Algebra I: Cellularity
This is the first of four articles studying some slight generalisations Hn m of Khovanov’s diagram algebra, as well as quasi-hereditary covers Kn m of these algebras in the sense of Rouquier, and…
Analogue of Kostant's u-cohomology formula for the general linear superalgebra
We determine in an explicit form the Lie superalgebra cohomology groups of the upper triangular odd subalgebra (Glm|n)+1 of the general linear superalgebra Glm|n with coefficients in irreducible…
...
...